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arXiv:0906.1758 · Journal of Physics Conference Series

Spin-wave theory for dimerized ferromagnetic chains

Alexander Herzog, Peter Horsch, Andrzej M. Oleś, Jesko Sirker

Published Jan 1, 2010• 3 citations
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Abstract

We describe a Peierls dimerization which occurs in ferromagnetic spin chains at finite temperature, within the modified spin-wave theory. Usual spin-wave theory is modified by introducing a Lagrange multiplier which enforces a nonmagnetic state at finite temperature. It is shown that this method gives results in excellent agreement with the density–matrix renormalization group applied to transfer matrices for dimerized ferromagnetic chains. We study bond correlation functions ( S i · S i+1 ) and explore the characteristic features of dimerization in the specific heat.

DOI
10.1088/1742-6596/200/2/022017

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Ferromagnetic, in contrast to antiferromagnetic, Heisenberg chains can undergo a spin-Peierls dimerization only at finite temperatures. They show reentrant behavior as a function of temperature, which might play a role for systems with small effective elastic constants as, for example, monatomic chains on surfaces. We investigate the physical properties of the dimerized ferromagnetic Heisenberg chain using a modified spin-wave theory. We calculate the exponentially decaying spin- and dimer-correlation functions, analyze the temperature dependence of the corresponding coherence lengths, the susceptibility, as well as the static and dynamic spin-structure factors. By comparing with numerical data obtained by the density-matrix renormalization group applied to transfer matrices, we find that the modified spin-wave theory yields excellent results for all these quantities for a wide range of dimerizations and temperatures.
We demonstrate that a Peierls dimerization can occur in ferromagnetic spin chains activated by thermal fluctuations. The dimer order parameter and entanglement measures are studied as functions of the modulation of the magnetic exchange interaction and temperature, using a spin-wave theory and the density-matrix renormalization group. We discuss the case where a periodic modulation is caused by spin-phonon coupling and the case where electronic states effectively induce such a modulation. The importance of the latter for a number of transition metal oxides is highlighted.
We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behaviour: at very low temperatures, the specific heat and the magnetic susceptibility multiplied by the temperature behave like and , respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give precise estimates for the low-temperature behaviour.
We study quantum spin-1/2 Heisenberg ferromagnetic chains with dilute random antiferromagnetic impurity bonds with the modified spin-wave theory. By describing thermal excitations in the language of spin waves, we observe a low-temperature Curie susceptibility due to the formation of large spin clusters first predicted by the real-space renormalization-group approach, as well as a crossover to a pure ferromagnetic spin-chain behavior at intermediate and high temperatures. We compare our results of the modified spin-wave theory to quantum Monte Carlo simulations.
The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as u a with a > 2 where u denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives even in the presence of randomness. The string order behaves as u 2β with β∼0.37 in agreement with the recent prediction of real space renormalization group theory (β=(3−5)/2≃0.382\beta =(3-\sqrt{5})/2 \simeq 0.382β=(3−5​)/2≃0.382). The physical picture of this behavior in this model is also discussed.
The magnetization process, the susceptibility, and the specific heat of the spin-1∕21∕21∕2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at m=1∕6m=1∕6m=1∕6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.